Sonic boom in the shadow zone: A geometrical theory of diffraction

Abstract

Geometrical acoustics predicts the amplitude of sonic booms only within the carpet. Inside the geometrical shadow zone, a nonlinear, geometrical theory of diffraction in the time domain is proposed. An estimation of magnitude orders shows that nonlinear effects are expected to be small for usual sonic booms. In the linear case, the matching to geometrical acoustics yields an analytical expression for the pressure near the cutoff. In the shadow zone, it can be written as a series of creeping waves. Numerical simulations show that the amplitude decay of the signal compares favorably with Concorde measurements, while the magnitude order of the rise time is correct. The ground impedance is shown to influence the rise time and peak amplitude of the signal mostly close to the cutoff. In the case of a weakly refractive atmosphere (low temperature gradient or downwind propagation), the transition zone about the cutoff is large, the transition is smooth, and the influence of ground absorption is increased.